THE DISTRIBUTION OF DARK-MATTER IN THE HALO OF M87

We investigate the constraints that can be placed on the distribution of dark matter around M87 using the 43 globular cluster velocities rep orted by Mould et al. [AJ, 99, 1823 (1990)]. If the globular cluster s ystem is assumed to be spherical, with an isotropic velocity distribut ion, we find that the most likely dependence of the dark matter densit y on radius is rho(r) is-proportional-to r-1.8 between about 3 and 30 kpc, where the exponent lies between 0.2 and 3.0 with 99% confidence. The total mass in the M87 halo within 50 kpc is 6.0(+4/-1) X 10(12) M. (90% confidence), consistent with current estimates from x-ray data. We estimate that a sample of roughly 200 velocities would be required to determine the exponent describing the mass density falloff to a pre cision of +/- 0.5 in a system like M87, under the isotropic hypothesis . The minimum number of velocities required to detect the presence of velocity anisotropy in the M87 globular cluster system is of order one thousand.